Earlier quoted context omitted.
That in itself is a problem because the ability for the voter to prove who they voted for opens them to coercion or bribery. Although doing it online (or by post) opens that risk anyway.
Can verify != can prove to a third party
Later, after the votes were tallied, the voter could verify that their ballot was (1) counted and (2) counted towards their chosen candidate. But crucially, all they could verify was that the vote counted towards position 1, or position 2, or position 3, ...
The point is that since the voter couldn't prove to a coercing party that the position they voted for was (or was not) the candidate the coercer wanted them to vote for, they were immune to coercion. They could prove that they voted for position 2, sure. But which candidate was at position 2?
The voter knows the truth because they saw the position list. However, until we have mind-reading technology, a coercing party could only take the voter's word.